A nitrile group-containing highly saturated copolymer rubber typified by a hydrogenated acrylonitrile-butadiene copolymer rubber is excellent in heat resistance, oil resistance, ozone resistance and the like as compared with a common nitrile group-containing copolymer rubber such as an acrylonitrile-butadiene copolymer rubber, having a plenty of carbon-carbon unsaturated bonds in the main chain structure thereof. However, on the other hand, a nitrile group-containing highly saturated copolymer rubber is sometimes inferior in cold resistance as compared with a nitrile group-containing copolymer rubber, depending on the nitrile group content or the proportion of the unsaturated bonds in the carbon-carbon bonds of the nitrile group-containing highly saturated copolymer rubber.
As such a nitrile group-containing highly saturated copolymer rubber, for example, Patent Document 1 has proposed a nitrile group-containing highly saturated copolymer rubber (A), comprising an α,β-ethylenically unsaturated nitrile unit (a), an α,β-ethylenically unsaturated carboxylic acid ester unit (b), a conjugated diene unit (c), and a saturated conjugated diene unit (d) each in a particular proportion, having a proportion of the saturated conjugated diene unit (d) of 70 wt % or more in relation to the total proportion of the conjugated diene unit (c) and the saturated conjugated diene unit (d), and having a difference between an extrapolated glass transition initiation temperature (Tig) and an extrapolated glass transition end temperature (Teg) of 10° C. or less. However, in a cross-linked rubber obtained by using the nitrile group-containing highly saturated copolymer rubber described in Patent Document 1, the cold resistance has been improved to some extent, but the resistance to swelling in oil and the resistance to hardening in oil have been insufficient.